4.4 Results and Analysis
85
129 MPa specimens, respectively. It indicates that ε
u
1 /ε
u
c and σ 3 /f
c show nearly a
linear relationship, and the function of the fitted straight line is
ε
u
1
ε
u
c = 1 + 6.24(σ 3 /f
c )
(4.1)
The slope of the fitted straight line is 6.24 for UHPCC. Moreover, Lu and Hsu
(2006), Ansari and Li (1998) and Candappa et al. (2001) did the same work and
also found the above linear relationship, while the slopes are 19.21, 15.15 and 20
for concrete specimens with f
c ranging from 32.6 MPa to 107.3 MPa, respectively.
It indicates that, for UHPCC material, the relatively larger magnitude of the peak
strain with the rising of the confinement ratio was not obvious compared with NSC
and HSC.
4.4.3 Failure Criteria
In this section, the triaxial compression test results of UHPCC from Table 4.2 were
used to calibrate the existing three most applied failure criteria.
4.4.3.1 Mohr–Coulomb Failure Criterion
Mohr–Coulomb failure criterion is a classical failure criterion for describing the
failure envelop, and is still extensively used due to its simplicity and relatively good
accuracy. The pressure-dependent Mohr–Coulomb model is expressed as
σ
u
1
f
c = 1 + k i σ 3
f
c
(4.2)
where k i = (1 + sin ϕ)
(1− sin ϕ) and ϕ represents the internal-friction angle of
concrete. The previous works indicate that the value of k i ranges from 2.6 to 5.3 for
concrete specimens with diverse strengths (Lu and Hsu 2006; Xie et al. 1995; Ansari
and Li 1998; Candappa et al. 2001; Lan and Guo 1997).
For the present test, shown in Fig. 4.7a, it is found that the best-fit value of k i for
the dimensionless peak axial stress-confining pressure relationship is 4.1. Figure 4.7b
also gives the existing compressive tests data on high-strength concrete, including
UHPCC, HPFRC and SIFCON as well as the curve of Eq. (4.2) with k i = 4.1 obtained
from Fig. 4.7a. The comparisons indicate that, (i) For HSC and the confining ratio
σ 3
f
c ≤ 1, the relationship of σ
u
1
f
c versus σ 3
f
c have nearly the same tendency,
and the influences of strength, size, compositions of specimens were not pronounced;
(ii) For low confinement levels (σ 3 /f c ≤ 0.5), k i = 4.1 can better predict the peak
axial stress values; (iii) For high levels of confinement (σ 3 /f c > 0.5), Mohr–Coulomb
failure criterion overpredicts the peak triaxial stress of HSC.
85
129 MPa specimens, respectively. It indicates that ε
u
1 /ε
u
c and σ 3 /f
c show nearly a
linear relationship, and the function of the fitted straight line is
ε
u
1
ε
u
c = 1 + 6.24(σ 3 /f
c )
(4.1)
The slope of the fitted straight line is 6.24 for UHPCC. Moreover, Lu and Hsu
(2006), Ansari and Li (1998) and Candappa et al. (2001) did the same work and
also found the above linear relationship, while the slopes are 19.21, 15.15 and 20
for concrete specimens with f
c ranging from 32.6 MPa to 107.3 MPa, respectively.
It indicates that, for UHPCC material, the relatively larger magnitude of the peak
strain with the rising of the confinement ratio was not obvious compared with NSC
and HSC.
4.4.3 Failure Criteria
In this section, the triaxial compression test results of UHPCC from Table 4.2 were
used to calibrate the existing three most applied failure criteria.
4.4.3.1 Mohr–Coulomb Failure Criterion
Mohr–Coulomb failure criterion is a classical failure criterion for describing the
failure envelop, and is still extensively used due to its simplicity and relatively good
accuracy. The pressure-dependent Mohr–Coulomb model is expressed as
σ
u
1
f
c = 1 + k i σ 3
f
c
(4.2)
where k i = (1 + sin ϕ)
(1− sin ϕ) and ϕ represents the internal-friction angle of
concrete. The previous works indicate that the value of k i ranges from 2.6 to 5.3 for
concrete specimens with diverse strengths (Lu and Hsu 2006; Xie et al. 1995; Ansari
and Li 1998; Candappa et al. 2001; Lan and Guo 1997).
For the present test, shown in Fig. 4.7a, it is found that the best-fit value of k i for
the dimensionless peak axial stress-confining pressure relationship is 4.1. Figure 4.7b
also gives the existing compressive tests data on high-strength concrete, including
UHPCC, HPFRC and SIFCON as well as the curve of Eq. (4.2) with k i = 4.1 obtained
from Fig. 4.7a. The comparisons indicate that, (i) For HSC and the confining ratio
σ 3
f
c ≤ 1, the relationship of σ
u
1
f
c versus σ 3
f
c have nearly the same tendency,
and the influences of strength, size, compositions of specimens were not pronounced;
(ii) For low confinement levels (σ 3 /f c ≤ 0.5), k i = 4.1 can better predict the peak
axial stress values; (iii) For high levels of confinement (σ 3 /f c > 0.5), Mohr–Coulomb
failure criterion overpredicts the peak triaxial stress of HSC.